Some structural properties of discrete surfaces

  • Gilles Bertrand
  • Michel Couprie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1347)


In the framework of combinatorial topology a surface is decribed as a set of faces which are linked by adjacency relations. This corresponds to a structural description of surfaces where we have some desirable properties: for example, any point is surrounded by a set of faces which constitute a “cycle”. The notion of combinatorial surface extracts these “structural” properties of surfaces.

In this paper, we introduce a relation for points in Z3 which is based on the notion of homotopy. This allows to propose a definition of a class of surfaces which are combinatorial surfaces. We then show that the main existing notions of discrete surfaces belong to this class of combinatorial surfaces.


surfaces discrete topology homotopy simple points 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Gilles Bertrand
    • 1
  • Michel Couprie
    • 1
  1. 1.Laboratoire PSINoisy-Le-Grand CedexFrance

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